Identify the intervals on which each quadratic function is positive Part 1
1. y = x^2 + 9x + 18
2. y = x^2 + 2x - 8
3. y = x^2 - 5x - 24

Answer:

1734

Step-by-step explanation:

1. cube root the volume

2. square that number

3. multiply by 6 sides

Answer: w=6

Step-by-step explanation: 1. Simplify. Distribute the -4 to the w and the -3. -4*w is -4w and -4*-3 is +12, so your left with 3w-4w+12=6.

2. simplify again. 3w-4w is -w.

3. -w+12=6. Subtract w to both sides, so its -w=-6. The negatives cancel out, so w just equals 6.

Center: (3, -2) , Vertices: (3±√(11), -2) , Cο-vertices: (3, -2±(3/2)√(11)) , Foci: (3±√(88), -2),

Length of major axis: 2a = 2√(11),

Length of minor axis: 2b = 2(3/2)√(11) = 3√(11).

To identify the center, vertices, co-vertices, foci, length of the major axis, and length of the minor axis, we need to rewrite the equation of the given ellipse in standard form, which is:

\((x-h)^2/a^2 + (y-k)^2/b^2 = 1\)

Where (h,k) represents the center of the ellipse, "a" represents the distance from the center tοa vertex along the major axis, "b" represents the distance from the center to a co-vertex along the minor axis, and "c" represents the distance frοm the center to a focus along the major axis.

Starting with the given equatiοn:

\(-9x^2 +y^2 - 54x + 4y -86 =0\)

We need to complete the square fοr both x and y terms:

\(-9(x^2 - 6x) + (y^2 + 4y) = 86\)

To complete the square fοr the x terms, we need to add and subtract the square of half of the coefficient of x, which is  \((6/2)^2 = 9\):

\(-9(x^2 - 6x + 9 - 9) + (y^2 + 4y) = 86\)

\(-9(x - 3)^2 + (y^2 + 4y) = 95\)

To complete the square fοr the y terms, we need to add and subtract the square of half of the coefficient of y, which is \((4/2)^2 = 4:\)

\(-9(x - 3)^2 + (y^2 + 4y + 4 - 4) = 95\)

\(-9(x - 3)^2 + (y + 2)^2 = 99\)

Now, we can rewrite the equatiοn in standard form:

\([(x-3)^2]/(11) + [(y+2)^2]/(99/4) = 1\)

From this form, we can identify the center, vertices, co-vertices, foci, and lengths of the major and minοr axes:

Center: (3, -2)

Vertices: (3±√(11), -2)

Cο-vertices: (3, -2±(3/2)√(11))

Fοci: (3±√(88), -2)

Length οf major axis: 2a = 2√(11)

Length οf minor axis: 2b = 2(3/2)√(11) = 3√(11)

Tο sketch the graph, we can plot the center at (3, -2), draw the major and minor axes, and then sketch the ellipse using the vertices and co-vertices as a guide. The foci should be inside the ellipse along the major axis.

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Answer:

To calculate how much will be in Tallulah's account after 6 weeks, we need to find out how much her balance will increase each week due to her steady deposits, and then add that to her current balance.

Since Tallulah is depositing $21.35 per week, her balance will increase by that amount each week. After 6 weeks, her balance will have increased by:

$21.35/week x 6 weeks = $128.10

To find out how much will be in her account after 6 weeks, we need to add the amount of her balance increase to her current balance:

-$39.35 + $128.10 = $88.75

So after 6 weeks of making steady deposits, Tallulah's account will have a positive balance of $88.75.

Answer: $88.75

b r a i n l i e s t ?

Answer:

B) x = -5

Step-by-step explanation:

The zero of a graph is the inputted value in which the output is 0. Therefore, we must find the x-value that makes the y-value be 0. In the graph, we see that y = 0 at (-5, 0). The x-value of the coordinate (-5, 0) is -5. Therefore, the zero of the function in the graph is x = -5.

I hope this helps! :)

Answer:

I thinks so

Step-by-step explanation:

Answer:

We know that the x-coordinate of point A is -11, and that the distance between point A and point B is 15 units. Let's call the y-coordinate of point A "y". Then we can use the distance formula to find the two possible values of y:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1,y1) = (-11,y) is the coordinates of point A, and (x2,y2) = (1,2) is the coordinates of point B. Substituting the values, we get:

15 = sqrt((-11 - 1)^2 + (y - 2)^2)

15 = sqrt(144 + (y - 2)^2)

15^2 = 144 + (y - 2)^2

225 = 144 + (y - 2)^2

81 = (y - 2)^2

y - 2 = ±9

y = 2 ± 9

So the possible coordinates of point A are (-11,11) and (-11,-7).

The value of d in the image that shows the two parallel lines that are crossed by the transversal is determined as: 125°.

In geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects a pair of parallel lines, it creates various angles and relationships between those angles.

The image attached below shows the two parallel lines which are crossed by the transversal, where angle d and 125° are vertical angles.

Since they are vertical angles, they will be equal or congruent to each other. Therefore, the value of d = 125°

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The amount that Sidney will have in her account in 1 year is $ 95,704.

Given that:-

Principal amount = $85,450

Interest Rate = 12 % per annum

i = prt

Where,

i represents interest,

p represents the principal,

r represents the interest rate, and

t represents the time (in years)

Hence, putting the values in the formula of simple interest, we get,

i = 85450*(12/100)*1 = $ 10,254

Hence, the amount that Sidney will have in her account in 1 year is

85450 + 10254 = $ 95,704

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Answer:

1/2

Step-by-step explanation:

See the steps below:)

Answer:

40x + 17(468-x) = 11912

       23x = 11912 - 17*468     |Solve for x and then find (468-x) as well

The value of y is 29. 2

Algebraic expressions are defined as mathematical expressions that are composed of terms, variables, factors, constants and coefficients.

These algebraic expressions are also made up of mathematical or arithmetic operations.

These arithmetic operations are;

From the information given, we have that;

y = 7.3x

If the value of x = 4

Substitute the values

y = 7.3(4)

expand the bracket

y = 29. 2

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Answer:

35

Step-by-step explanation:

You can easily graph this in desmos for a visual understanding.

The slope of a line is received by (y2-y1)/(x2-x1). Assuming that Days is X and the cost is Y, we get (160-90)/(4-2), and it makes 70/2, which equates out to 35. Because the prices become more and more expensive, the slope is positive 35.

Answer:

5/9 not sure if correct sorry if wrobg

Answer:

9/5

Step-by-step explanation:

Solution

3

2

​

5

6

​

​

=?

Step 1. Multiply the numerator by the reciprocal of the denominator.

=

3

2

​

5

6

​

​

=

5

6

​

×

2

3

​

=

5×2

6×3

​

Step 2. Simplify by dividing top and bottom by the highest common factor (2)

5×2

6×3

​

=

5×1

3×3

​

∴

3

2

​

5

6

​

​

=

5

9

​

The value of measure of x in the triangle is,

⇒ x = 4√3 units

We have to given that,

A triangle is shown in image.

Now, WE can formulate by trigonometry formula we get;

⇒ tan 30° = Opposite / Base

⇒ tan 30° = 4 / x

⇒ 1/√3 = 4/x

⇒ x = 4√3 units

Thus, The value of measure of x in the triangle is,

⇒ x = 4√3 units

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Answer:

0.8 gallons per second

Step-by-step explanation:

Given that :

Filling occurs at a constant rate ;

Change in gallon of water in pool within a 3 seconds time interval ;

Assume :

At t = 0 ; gallons = 5

At t = 3 ; gallons = 7.4

Chanhe in gallons with time.;

(7.4 - 5) / (3 - 0)

2.4 / 3

= 0.8 gallons per second

Answer:

Step-by-step explanation:

3x^2 = -12

x^2 = -4

x = ±√-4

this equation has no real solutions

Answer:

-------------------------------

Answer:

slope (m) = 2/3

Step-by-step explanation:

slope = change in x /change in y

Also, slope is y2 - y1 / x2 -x1. That is what I apply for this activity, hence:

slope = 3 - (-1) / 0 - (-6)

         = 3 + 1 / 0 + 6

         = 4 / 6

         = 2/3

∴ slope(m) = 2/3

Answer: the volume is 480 cm

Step-by-step explanation:

You find the volume of a shape by multiplying the base x width x height. In this case the height is 6 the width is 8 and the length is 10. 6x8x10= 480.

Answer:

lb×bh×hl

6×8×8×10×10×6

48×80×60

230400

Answer: 51/50

Step-by-step explanation:   102/100 = 51/50

because you divide both by 2 which is the answer

Answer:

y=-5/2x+12

Step-by-step explanation:

We know that the slope is -5/2 and the line passes through (8,-8). We can use the slope in the equation y=-5/2x+b and the given point to find for b. Plug in (8,-8) as x and y values to get -8=-5/2(8)+b. Multiply to get -8=-20+b, then add 20 to both sides to get 12=b. You can then use b to complete your equation, y=-5/2x+12.

Answer

its scale factor is ​4/3 and 0.75

Step-by-step explanation:

The valid numbers that satisfy all the given inequalities are -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6.

Let's solve each inequality step by step:

1. Two less than a number (x) is no more than 5:

The inequality is given as x - 2 ≤ 5. Adding 2 to both sides, we get x ≤ 7. This means that any number less than or equal to 7 satisfies the inequality.

2. Seven subtracted from 4 times a number (x) is more than 13:

The inequality is given as 4x - 7 > 13. Adding 7 to both sides, we get 4x > 20. Dividing both sides by 4, we obtain x > 5. So any number greater than 5 satisfies the inequality.

3. The sum of two times a number (x) and -2 is at least 8:

The inequality is given as 2x - 2 ≥ 8. Adding 2 to both sides, we get 2x ≥ 10. Dividing both sides by 2, we have x ≥ 5. So any number greater than or equal to 5 satisfies the inequality.

4. Four added to 3 times a number (x) is less than 19:

The inequality is given as 3x + 4 < 19. Subtracting 4 from both sides, we get 3x < 15. Dividing both sides by 3, we obtain x < 5. So any number less than 5 satisfies the inequality.

Based on the above solutions, the valid numbers that satisfy all the given inequalities are -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6. These numbers can be represented on a number line graph by marking the appropriate points and shading the corresponding regions.

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Step-by-step explanation:

It's just asking you to rewrite it in vertex form. Which would be

\((x + 10) ^{2} - 4\)

Answer:

a) {3,5}{3,10}{5,10}

b) \(P(A)=\frac{1}{3}\)

c) \(P(B)=\frac{2}{3}\)

d) \(P(C)=\frac{1}{3}\)

e) \(P(A and C)=0\)

f) \(P(A or B)=1\)

g) \(P(B and C)=\frac{1}{3}\)

h) \(P(A or C)=\frac{2}{3}\)

i) \(P(C given B)=\frac{1}{2}\)

j) \(P(C given A)=0\)

k) \(P(not B)=\frac{1}{3}\)

l) \(P(not C)=\frac{2}{3}\)

Yes, events A and B are mutually exclusive. Because the results can either be even or odd, not both. No, events B and C are not mutually exclusive because the result can be both, odd and prime.

Step-by-step explanation:

a)

In order to solve part a of the problem, we need to find the possible outcomes, in this case, the possible outcomes are:

{3,5}{3,10} and {5,10}

We could think of the oppsite order, for example {5,3}{10,3}{10,5} but these are basically the same as the previous outcomes, so we will just take three outcomes in our sample space. We can think of it as drawing the two chips at the same time.

b)

Now the probability of the sum of the chips to be even. There is only one outcome where the sum of the chips is even, {3,5} since 3+5=8 the other outcomes will give us an odd number, so:

\(P=\frac{#desired}{#possible}\)

\(P(A)=\frac{1}{3}\)

c) For the probability of the sum of the chips to be odd, there are two outcomes where the sum of the chips is odd, {3,10} since 3+10=13 and {5,10} since 5+10=15 the other outcomes will give us an even number, so:

\(P(B)=\frac{2}{3}\)

d) The probability of the sum of the chips is prime. There is only one outcome where the sum of the chips is prime, {3,10} since 3+10=13 the other outcomes will give us non prime results, so:

\(P(C)=\frac{1}{3}\)

e) The probability of the sum of the chips to be even and prime. There are no results where we can get an even and prime number, since the only even and prime number there is is number 2 and no outcome will give us that number, so:

P(A and C)=0

f) The probability of the sum of the chips is even or odd. We can either get even or odd results, so no matter what outcome we get, we will get an odd or even result so:

\(P(A or B)=1\)

g) The probability of the sum of the chips is odd and prime. There is only one outcome where the sum of the chips is odd and prime, {3,10} since 3+10=13 the other outcomes will give us non prime results, so:

\(P(B and C)=\frac{1}{3}\)

h) The probability of the sum of the chips is even or prime. There are two outcomes where the sum of the chips is even or prime, {3,10} since 3+10=13 and {3,5} since 3+5=8 so:

\(P(A or C)=\frac{2}{3}\)

i) The probability of the sum of the chips is prime given that the sum of the chips is odd. There are two possible results where the sum of the chips is odd {3,10} and {5,10} and only one of those results is even, {3,10}, so

\(P(C given B)=\frac{1}{2}\)

j) The probability of the sum of the chips is prime given that the sum of the chips is even. There is only one possible even result: {3,5} but that result isn't prime, so

\(P(C given A)=0\)

k) The probability of the sum of the chips is not odd. There is only one outcome where the sum of the chips is not odd (even), {3,5} so:

\(P(not B)=\frac{1}{3}\)

l) The probability of the sum of the chips is not prime. There are two outcomes where the sum of the chips is not prime, {3,5} and {5,10} so:

\(P(not C)=\frac{2}{3}\)

Are events A and B mutually exclusive?

Yes, events A and B are mutually exclusive.

Why or why not?

Because the results can either be even or odd, not both.

Are events B and C mutually exclusive?

No, events B and C are not mutually exclusive.

Why or Why not?

Because the result can be both, odd and prime.

Answer:

\(70f^{3}g^{2}h\)

Step-by-step explanation:

Answer:

The answer- 1254ft

Step-by-step explanation:

You can do the calculator trick and get the answer and round to the tenth

The worker recieves 3 hours of break time per day.

Given is that a a fast-food worker works Monday through Friday, 8 hours per day. Daily, the worker receives a hour break in the morning, a hour break for lunch, and a hour break in the afternoon.

The worker recieves three breaks, meaning it recieves 3 hours of break time per day.

Therefore, the worker recieves 3 hours of break time per day.

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